Delegating Capabilities in Predicate Encryption Systems

In predicate encryption systems, given a capability, one can evaluate one or more predicates on the plaintext encrypted, while all other information about the plaintext remains hidden. We consider the role of delegation in such predicate encryption systems. Suppose Alice has a capability, and she wishes to delegate to Bob a more restrictive capability allowing the decryption of a subset of the information Alice can learn about the plaintext encrypted. We formally define delegation in predicate encryption systems, propose a new security definition for delegation, and give an efficient construction supporting conjunctive queries. The security of our construction can be reduced to the general 3-party Bilinear Diffie-Hellman assumption, and the Bilinear Decisional Diffie-Hellman assumption in composite order bilinear groups.